>> what you are describing here is the structure of the> natural numbers as a directed set.>> There is actual mathematics that describes this.>> There are logics in which your reasoning can be> formalized.

That is not necessary for pople who can think without crutches.>> And the fact that this structure remains as absolute> infinity relative to Cantor's transfinite arithmetic> does not make that arithmetical calculus not> mathematics.

Cantor has been disproved. Try to understand the Binary Tree. Then youwill understand that not more than countably many paths can bedistinguished.

Here is a summary of the argument concerning the Binary Tree:

1) The set of all real numbers of the unit interval is (said to be)uncountable.2) An uncountable set has (infinitely many) more elements than acountable set.3) Every real number has at least one unique representation as aninfinite binary string (some rationals have even two representationsbut that's peanuts).4) In many cases the string cannot be defined by a finite word.5) Without loss of information the first bits of two strings, ifequal, need not be written twice.6) Application of this rule leads to the Binary Tree.7) The binary strings of the unit interval are isomorphic to the pathsof the Binary Tree.8) It is not possible to distinguish more than countably many paths bytheir nodes.9) This is proven by constructing the Binary Tree node by node.10) Further this is proven by colouring all edges and nodes and pathsof the complete Binary Tree by countably many paths.